The generator matrix

 1  1  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0 X^3  0  0 X^3 X^3  0
 0  0 X^3  0  0 X^3  0 X^3 X^3  0  0
 0  0  0 X^3  0 X^3 X^3 X^3  0  0  0
 0  0  0  0 X^3 X^3 X^3  0  0 X^3  0

generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+9x^8+6x^10+224x^11+6x^12+9x^14+1x^22

The gray image is a linear code over GF(2) with n=88, k=8 and d=32.
This code was found by Heurico 1.16 in 6.87e-008 seconds.